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超表面具有纳米级的光操纵能力,与其他方法相比,用超表面产生涡旋具有结构紧凑、厚度较薄、易于控制和集成的优点。通过精心设计,可以在离超表面较远的地方得到光涡旋,也称之为非局域涡旋。超表面纳米结构的尺寸、形状改变以及各向异性纳米结构的旋转可以使透射场具有额外的相位延迟。超表面对相位的调控可以简要分为动力学相位(Dynamic phase)和几何相位(Geometric phase)两类[44],或更详细地划分为几何相位、共振相位与传输相位三类[45],文中采用简要划分。
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累积传播效应产生的相位变化依赖于传播距离与给定介质的折射率。利用超薄亚波长纳米结构(也称为超表面)沿界面引入不连续相位(Phase discontinuity)时,可以根据广义斯涅尔定律控制反射和折射[35]:
$$\left\{ \begin{array}{l} \sin \left( {{\theta _t}} \right){n_t} - \sin \left( {{\theta _i}} \right){n_i} = \lambda \dfrac{{\nabla \phi }}{{2\pi }} \\ \sin \left( {{\theta _r}} \right){n_i} - \sin \left( {{\theta _i}} \right){n_i} = \lambda \dfrac{{\nabla \phi }}{{2\pi }} \\ \end{array} \right.$$ (1) 式中:θt、θi、θr分别为折射角、入射角、反射角;nt和ni分别为介质在透射侧和入射侧的折射率;
$\nabla $ ϕ为沿着界面的相位梯度变化。这种相位不连续性可以通过亚波长尺度的金属纳米天线、散射体或薄膜来实现。通过激发不同几何形状谐振器的局部等离子共振,散射场会引导或延迟激发场,从而导致相位不连续的调谐。由于单个纳米天线产生的非方向性散射电场,这种调谐被限制在0~π范围内[40-41, 46]。通过使用多层超表面、具有多重独立共振的散射体或耦合天线共振,能够在不改变偏振的情况下将相位调谐扩展到整个2π范围[47-49]。与传统的相位积累效应相比,这种突变相位由可忽略厚度的谐振腔引入。对界面的相位剖面进行设计,可以通过超表面产生带有螺旋相位波前的涡旋光束。图2(a)为排布在八个扇形区域不同尺寸的纳米单元[47],单元由在银膜上圆孔中填充介电材料组成。通过改变纳米孔半径激发谐振散射场和波导模式,从而实现可覆盖2π范围的相位调谐,对称的几何结构保证了对激发偏振场的不敏感性。由于在光频率上有明显的欧姆损耗和吸收,因此这种装置转换的涡旋光束的传输功率很低。此外,与自由空间阻抗的失配导致背反射,降低了转换效率[48-50]。为了高效率的产生涡旋,可以用较厚的高折射率介质材料代替金属[51-54]。图2(b)为一个偏振无关的硅超表面,通过对硅纳米盘电偶极共振和磁偶极共振的重叠得到高效的惠更斯超表面,所需的2π范围相位变化可以通过改变纳米磁盘阵列的晶格间距实现[55]。
由上述超表面产生的涡旋光束在传播过程中通常携带固定的轨道角动量。但是近期出现了一些例外情况,涡旋光束的拓扑电荷会随光束的传播而变化。特殊的费马螺旋使局域拓扑电荷在长距离传播过程中发生变化[56],相位的变化由传播距离控制。根据标量衍射理论,金属螺旋结构在距离物平面z处的透射场可以近似写为:
$$u {\rm{(}}x{\rm{,}}y{\rm{,}}{\textit{z}}{\rm{)}} = \iint {u {\rm{(}}{x_{\rm{0}}}{\rm{,}}{y_{\rm{0}}}{\rm{,}}{\textit{z}}{\rm{)}}}\frac{{{{\rm{e}}^{ik\rho }}}}{\rho }{\rm{cos}}\theta {\rm{d}}{x_{\rm{0}}}{\rm{d}}{y_{\rm{0}}}$$ (2) 式中:u(x0, y0, z)为螺旋狭缝后传输场的振幅;cosθ=z/ρ为倾斜因子;ρ=[(x–x0)2+(y–y0)2+z2]1/2为物体点到观测点的距离,对于沿传播轴的观测点,可以根据螺旋轨迹进行简化。由于相邻两物点到观测点的相位差与传播距离有关,观测点周围光场的相位差必然与传播距离有关,并直接影响光涡旋。类似的,采用轨道半径满足r=r0+lλSPPφ的阿基米德螺旋缝也可以实现随传播距离变化的光涡旋[57],螺旋缝产生的涡旋光束仍与传播距离有关,拓扑电荷的值随传播距离的增大而减小,通过调节螺线几何结构和传播距离的大小可以控制拓扑电荷的值。
除了在远场产生可变拓扑荷的涡旋光外,在金属表面刻蚀螺线结构也被广泛应用于产生等离激元涡旋[58-59]。当光入射金属表面的结构时,可以激发局域在金属与电介质界面的沿界面传播的表面等离子体极化激元(Surface Plasmonic Polaritons,SPP)。远离金属表面后,表面等离激元就像倏逝波一样迅速衰减。结构激发的等离涡旋可以看作所有SPP场的叠加场,该涡旋场由于SPP场的局域性而成为局域场。获得等离激元涡旋更直接的方法是利用圆偏振光照射圆形纳米缝,光子的自旋角动量将与纳米缝耦合成为轨道角动量。光子自旋角动量与轨道角动量的耦合被定义为光自旋霍尔效应[60-61]。纳米缝可以为特定的单孔或双孔,孔结构可以是简单的圆形、矩形甚至z形等[62-63]。
若要获得高阶等离激元涡旋,需要引入更多的附加相位。一种方法是调整螺线轨迹起始和结束之间的间隙lλspp引入附加相位[58],l为附加拓扑荷数,λspp为SPP的波长。需要指出的是,任何一个带较大拓扑荷l的螺线产生的高阶等离涡旋都存在缺陷。这是由于SPP场在沿金属表面传播过程中衰减,而传播距离取决于金属的吸收,l的值越大,缺陷越明显。可以用分段螺旋代替整个螺旋对此进行改进,从而改善生成的高阶等离激元涡旋[64-66]。此外,可以通过纳米孔引入几何相位项,从而改变涡旋光束的拓扑荷[67]。值得注意的是,当引入的几何相位过大时,传输场涡旋光束会发生畸变,适当增大圆轨迹的半径可以解决这一问题。
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除了以上提到的动力学相位外,还可以引入Pancharatnam-Berry (P-B)相位,即通过旋转尺寸相同的各向异性结构单元来产生几何相位[68-69],任意不同旋转角度的纳米天线产生的散射波相位差等于它们旋转角度差的2倍。利用P-B相位产生涡旋的优点是它不依赖于结构的尺寸、固有的材料色散或结构共振,只通过旋转各向异性纳米结构单元的光轴来控制。考虑垂直入射下沿光轴旋转的纳米天线,其传输系数可用琼斯矩阵表示:
$$T = \left( {\begin{array}{*{20}{c}} {{a_x}{{\cos }^2}\alpha + {a_y}{{\sin }^2}\alpha {{\rm{e}}^{j\delta }}}&{({a_x} - {a_y}{{\rm{e}}^{j\delta }})\sin \alpha \cos \alpha } \\ {({a_x} - {a_y}{{\rm{e}}^{j\delta }})\sin \alpha \cos \alpha }&{{a_x}{{\sin }^2}\alpha + {a_y}{{\cos }^2}\alpha {{\rm{e}}^{j\delta }}} \end{array}} \right)$$ (3) 式中:ax和ay为光场沿两个主轴方向的振幅分量;δ为两分量的相位差;α表示快轴方向与x轴方向的夹角。对于给定的入射光(i1, i2),利用偏振基转换[70]可以得到圆偏振基下的透射场tc:
$${t_c} = \frac{A}{2}\left( \begin{array}{l} {i_1} \\ {i_2} \\ \end{array} \right) + \frac{B}{2}{i_2}{{\rm{e}}^{ - j2\alpha }}\left( \begin{array}{l} 1 \\ 0 \\ \end{array} \right) + \frac{B}{2}{i_1}{{\rm{e}}^{j2\alpha }}\left( \begin{array}{l} 0 \\ 1 \\ \end{array} \right)$$ (4) 式中:A=ax+ayejδ; B=ax−ayejδ。利用P-B相位超表面调控光场的过程可以用上述公式来描述。
第一项表示与入射偏振相同的偏振状态,第二项表示左旋圆偏振态,第三项表示右旋圆偏振态,三者振幅的幅度是不同的。其中,后两项存在附加相位e±j2α,这种相位即结构旋转引起的几何相位。通过对各向异性纳米天线的转角α从0旋转到π,入射光的交叉偏振光相移从0~2π进行调谐。此外,由于每个单元的几何形状不变,散射振幅也保持不变。利用这种附加相位控制透射光的波前便可以得到相应的涡旋光束。图3为Karimi E等人基于P-B相位在可见光照明下设计的产生涡旋光束的超表面结构[71]。等离纳米天线的取向角沿着同心圆环旋转2π,赋予交叉偏振光从0~4π的相位变化,从而产生二阶的光学涡旋。此外,产生的拓扑荷与入射光偏振状态相关,左旋和右旋圆偏振入射光所产生光学涡旋的拓扑电荷分别为l=+2和l=−2。通过所产生的光学涡旋分别与平面波、球面波的干涉验证了涡旋光的拓扑荷值。
各向异性纳米孔的旋转不仅可以使相位绕光轴发生角向变化以产生涡旋,还可以实现更加灵活的相位响应。图4为利用矩形孔旋转实现不同相位叠加得到超表面,它可以生成完美涡旋光束,环状光强的大小不受涡旋光拓扑荷的影响[72]。图4(a)为超表面结构对应叠加后的相位剖面与制得样品的SEM图,所得透射场的强度与涡旋干涉图样分别如图4(b)和图4(c)所示。可以看出,环状光强的半径不随拓扑荷的变化而改变。
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纳米结构的动力学相位和几何相位相结合为相位调制提供了更大的自由度。几何相位的宽带特性被用来补偿金属和介电纳米结构耦合共振的色散,使器件能够在宽光谱范围内工作。在设计全波控制的混合超表面时,单次或局部谐振不足以改变相位,除了调整多个谐振腔或相邻散射体间的耦合强度外,还可以引入几何相位。
图5(a)展示了一种V形金属纳米天线,该天线通过改变结构的臂长、两臂的张角产生0~π的相位变化并旋转结构实现了2π的相位覆盖。如图5(b)所示,四种不同的V形纳米天线排布在八个扇形区域组成超表面,利用单元旋转引入几何相移,相位绕光轴实现了完整的2π相位变化,这是第一个被实验证明的纳米结构[35]。该超表面引入螺旋状相移,从而使正入射的线性偏振光产生l = 1的涡旋光束。涡旋光束在远场呈环形强度分布,暗中空区域对应相位奇点。与共轴的高斯光束干涉,显示出涡旋光束的螺旋波前,产生螺旋干涉图;与倾斜的高斯光束干涉时则产生一个错位的干涉条纹。类似的,在不同扇形区域内布置覆盖2π倍数相位变化的纳米结构就会产生高阶涡旋光束。如图5(c)和图5(d)所示,不同角度、不同长度的V形天线按不同排序分为三组,对相移的调控分别覆盖2π、4π、6π。在七个扇形区域排列形成超表面,可以得到拓扑荷分别为1、2和3的涡旋光[73]。
图 5 (a) V型光学纳米天线的相位调控能力[35];(b)八种V型纳米天线组成超表面涡旋发生器与透射光干涉图样[35];(c)三组V型天线交叉偏振中的相移和幅值;(d) V型纳米天线组成的高阶涡旋发生器[73]
Figure 5. (a) Phase control ability of V-shaped optical nantennas[35]; (b) Metasurface vortex generator composed of 8 V-shaped nantennas and the interference patterns[35]; (c) Phase shift and amplitude in cross polarization of 3 group V-shaped antennas; (d) High-order vortex generator composed of V-shaped nantennas[73]
相位梯度超表面能方便地将不同轨道角动量传递到光束中,为研究复杂动量耦合的影响提供了便利。2017年,Capasso等人提出了一种实现任意自旋到轨道角动量转换的方法[74]。超表面通过同时控制结构快轴的方向角和相移来实现这一功能,结构如图6(a)所示。之后他们利用这种方法设计了一种能分别将左右旋圆偏振光转换为携带不同OAM值光学涡旋的超表面,并进行了实验验证。
图 6 (a)任意自旋轨道角动量转换的概念与结构示意图[74];(b)周期性圆环超表面功能与结构示意图[75];(c)超表面叉形光栅相位分布、SEM图和产生的光学涡旋[78]
Figure 6. (a) Schematic of the arbitrary spin-to-orbital angular momentum conversion[74]; (b) Schematic of the structure and function of periodic-rings metasurface[75]; (c) Phase distribution, SEM image and generated optical vortices of a metasurface fork-shaped grating[78]
同样是利用不同相位的结合,在超表面中将等离子体延迟相位与几何相位相结合,为产生高纯度的涡旋光束提供了一种新途径[75]。如图6(b)所示,超表面由在银膜上刻蚀的多个周期性圆环构成,其半径定义为Rn = R1 + (n−1)P,其中n和P表示孔径的数目和周期,环形孔可以看作是一组空间方向变化的纳米缝的二维扩展。当圆偏振光正入射在这种非均匀、各向异性的超表面上时,旋向相反的透射光具有特定的相位分布。这项工作克服了不连续的相位分布在散射场中引入相位噪声,降低涡旋光束纯度的问题。此外,还可以通过混合相位来实现更为复杂的功能,比如高效地产生艾里涡旋光束 [76-77],在单个超薄元件上根据不同SAM产生和分裂涡旋光束[78-80]等。P-B相位沿界面形成相位梯度,表现为光子自旋霍尔动量偏移[81-85]。以超表面叉形光栅为例,如图6(c)所示,这种超表面叉形光栅在分裂自旋的同时能够产生光涡旋,H表示入射或透射的激光器具有水平偏振,LCP和RCP为入射或透射光束的偏振态[78]。
Generation of optical vortex beams via metasurfaces (Invited)
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摘要: 涡旋光束因为携带轨道角动量,在光通信、粒子操纵及量子信息等领域都具有重要的应用前景。目前有很多方法可用于产生涡旋光束,如利用螺旋相位板、模式转换、空间光调制器等。然而,传统的方法需要搭建体积相对较大的光学系统,限制了其在集成光学等领域中的应用。不同于传统方法中通过传输效应来获得相位变化,超表面可以通过纳米结构使入射光产生相位突变,在纳米尺度上独立控制动态或几何相位以产生涡旋。超表面具有强大光控制能力的同时,还具有体积小、易于集成等特点,因此成为了产生涡旋光的理想方法。文中在介绍产生涡旋光束基本原理的基础上,回顾了近年来利用超表面产生涡旋光束的研究进展。首先介绍了利用动力学相位、Pancharatnam-Berry (P-B)相位以及混合相位产生光学涡旋的方法。随后,对利用全息与编码超表面产生涡旋及通过多路复用产生多个涡旋等不同方法进行了综述。最后,对基于超表面产生涡旋的一些亟待解决的问题和应用前景作了简单总结与讨论。Abstract: Optical vortex beams, carrying orbital angular momentum, possess tremendous advanced applications ranging from optical communication, micromanipulation and nonlinear optics to quantum information. Various methods have been proposed to generate optical vortices, such as spiral phase plate (SPP), mode converter and spatial light modulator (SLM). However, changing phase by accumulating propagation distance restrains the applications in integrated optics. Owing to the salient properties that metasurface is small-sized and easy to be integrated, it is expected to be an ideal optical vortices generator with excellent ability of regulating light field. The basic principles of generating vortex beams and recent progress in the use of metasurfaces were introduced in this article. First, methods of using dynamic phase, Pancharatnam-Berry (P-B) phase and hybrid phase to generate optical vortices were introduced. Subsequently, holography and encoding metasurfaces and multiplexing metasurfaces were reviewed to generate multiple vortices. Finally, based on the generation of optical vortices via metasurfaces, some potential applications and problems were briefly summarized and discussed.
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Key words:
- optical vortices /
- orbital angular momentum /
- metasurface /
- generation methods
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图 5 (a) V型光学纳米天线的相位调控能力[35];(b)八种V型纳米天线组成超表面涡旋发生器与透射光干涉图样[35];(c)三组V型天线交叉偏振中的相移和幅值;(d) V型纳米天线组成的高阶涡旋发生器[73]
Figure 5. (a) Phase control ability of V-shaped optical nantennas[35]; (b) Metasurface vortex generator composed of 8 V-shaped nantennas and the interference patterns[35]; (c) Phase shift and amplitude in cross polarization of 3 group V-shaped antennas; (d) High-order vortex generator composed of V-shaped nantennas[73]
图 6 (a)任意自旋轨道角动量转换的概念与结构示意图[74];(b)周期性圆环超表面功能与结构示意图[75];(c)超表面叉形光栅相位分布、SEM图和产生的光学涡旋[78]
Figure 6. (a) Schematic of the arbitrary spin-to-orbital angular momentum conversion[74]; (b) Schematic of the structure and function of periodic-rings metasurface[75]; (c) Phase distribution, SEM image and generated optical vortices of a metasurface fork-shaped grating[78]
图 8 (a)超表面单元结构与产生多路涡旋光束示意图[96];(b)基于达曼光旋涡光栅涡旋光束OAM自由空间光通信的组合与分解示意图[98]
Figure 8. (a) Schematic of metasurface units and the generation of multiple vortex beams[96]; (b) Schematic of OAM-based free-space optical communications using the Dammann optical vortex grating for multiplexing/demultiplexing[98]
图 9 (a)共享孔径概念示意图,分割、交错和谐波响应几何相位超表面的远场强度分布[101];(b)分区域涡旋发生器强度分布和相应的干涉图样[102];(c)多通道交错相位超表面的SEM图与实验结果[103];(d)基于介电超表面的三维涡旋阵列的产生和重建[107]
Figure 9. (a) Shared-aperture phased antenna array. Far-field intensity distribution of segmented, interleaved, and harmonic-response metasurfaces[101]; (b) Intensity distribution and interference pattern of segmented vortex generator[102]; (c) SEM image of the metasurface and experimental results of multichannel interleaved phase[103]; (d) Generation and reconstruction of the 3D vortex array based on a dielectric metasurface[107]
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